This invention relates generally to the configuration of transonic aircraft with wings designed for extensive natural laminar flow (NLF), and more particularly to optimization of wing thickness, sweep and fuselage cross section relationship criteria, for such transonic aircraft.
There is need to improve the fuel efficiency and reduce carbon emissions of aircraft. Natural laminar flow (NLF) has been identified as a key technology in improving performance of aircraft through reduced drag, but there is a presumption that the reduced wing sweeps generally used to maintain natural laminar flow necessarily require a reduction in cruise speeds below Mach 0.80, and efficient aircraft of the future will be slower to foster efficiency. The invention described allows more efficient wings to be designed at current and higher speeds, e.g. Mach 0.80 to about Mach 1.2 Principal features are low to moderate sweep, and relatively thin airfoils in terms of the ratio of maximum thickness to chord (t/c). The importance of laminar boundary layer (BL) flow in terms of drag reduction can be understood by considering that for typical transonic cruise flight conditions the laminar skin friction drag is approximately a factor of ten less than turbulent skin friction drag associated with a traditional swept wing designs, for the same amount of surface area. At least equally important, the transonic NLF wing configurations described here can achieve best efficiency at higher Mach numbers than possible with the swept wings hitherto used on high speed subsonic aircraft.
For extensive NLF, the wing must have low or moderate sweep, and thus, on a purely aerodynamic basis the low sweep NLF wing should be as thin as needed to limit the volume wave drag at the design cruise Mach number. On the other hand a thinner wing incurs a weight penalty, since structural weight varies inversely with wing thickness, so that selection of thickness to chord ratio (t/c) is a key to optimizing the performance of such aircraft.
In previous studies, the NLF wing was designed to give best efficiency at about Mach 0.95 or higher. This work formed certain bases for U.S. Pat. No. 7,000,870, “LAMINAR FLOW WING FOR TRANSONIC CRUISE”, incorporated herein by reference. This Mach number criterion led to the selection of about 3% (0.03) as an upper limit for the span-wise average t/c ratio of the NLF wing.
This prior patent specified no variation of t/c with design cruise Mach number. More recently, design studies have covered a range of efficient cruise Mach numbers down to about 0.80, which is near the maximum efficient cruise Mach number of any previous or current swept wing subsonic aircraft designed for long range. Based on continued research to design low and moderate sweep laminar flow wings for supersonic aircraft, some relationships have been discovered allowing increases in wing aspect ratio for given levels of Mach, t/c, and sweep not contained in prior art for aircraft designed for transonic and supersonic Mach numbers.
A common measure to compare the rise of drag of a wing as the Mach number approaches a value of 1.0 is the “drag divergence” Mach number (Mdd), which is commonly defined as the Mach number at which the drag coefficient of the wing has increased by 0.0020 (20 counts) relative to the low Mach drag for the same lift condition. Drag divergence Mach is a measure of the point of significant reduction in wing efficiency, although many aircraft are designed to cruise at Mach numbers somewhat higher than Mdd. The variation of maximum t/c vs Mdd for well designed airfoils with zero sweep can be approximated by,(t/c)≦0.48(0.992−Mdd)
The well known effect of sweep in increasing Mdd is a non-linear function, with 20 degrees increasing Mdd approximately ˜0.03, 30 degrees ˜0.06, and 45 degrees ˜0.11. An unstated assumption of the traditional value of high wing sweep for transonic and supersonic Mach numbers is the requirement for a practical wing structure of sufficient span to generate lift at acceptable drag. Said wing constitutes a beam structure whose lift loads along the span generate bending moments which require thickness to react at acceptable weight levels. In addition, the airloads acting along the wing vary along the streamwise chord direction generating torsional twisting moments which also require finite thickness to resist. Were it possible to design a practical wing with zero thickness, there would be no advantage for sweep at transonic Mach numbers as the volume wave drag would be zero. In practical wings, the long span and minimum thickness desired for aerodynamic efficiency is limited structurally as a function of the thickness along that span.
Aspect ratio (A) is defined as the square of the wingspan (B) divided by the reference area (S). Wings designed at the upper extremes of aspect ratio to minimize lift dependent drag generally become flutter or divergence critical, and additional structural material with added weight must be incorporated.
Pioneering work on the relationship of aerodynamics and structures in flutter and divergence on subsonic high aspect ratio wings was done by the NACA's Theodorsen and Garrick in the 1930's and 1940's. Subsequently, compressible flow was found to have a significant exacerbating effect on flutter and divergence for wings which operate in the transonic regime. The basic aero-elastic relationships of Theodorsen and Garrick were extended to low aspect ratio transonic and supersonic regime wings by Martin in 1958 as described in NACA TN 4197. In that work Martin derived simple relationships for the fundamental forces and structural stiffness and related them to a large test database of high speed low aspect ratio wings. Martin derived a key non-dimensional parameter that allows initial approximation of the wing stiffness requirements to resist flutter or divergence in the transonic regime:X=39.3(Ap3)/[(t/c)3(Ap+2)]
where Ap is the “panel aspect ratio” based on the exposed wing semi-span and trapezoidal area cantilevered from the side of an aircraft body. The t/c was based on the t/c at approximately 75% of the spanwise distance from the aircraft centerline to the wing tip. The (Ap+2) component of the denominator in Martin's work was derived from the basic relation to calculate lift curve slope (α):α=2πA/(A+2)
When calculating lift curve slope based on the panel aspect ratio Ap (body side to tip) rather than the traditional aerodynamic tip-to-tip aspect ratio (A), however, the lift curve slope becomes:α=2πAp/(Ap+1)
For the panel aspect ratios of interest (approximately 1 to 6), this function's basic proportionality can be approximated by a simplified wing geometry parameter, ATC defined as follows:ATC=Ap0.78/(t/c)where the terms in the formula for ATC are defined above. When using panel aspect ratio, the (t/c) as measured at a section located 70% of the distance outboard of the aircraft body corresponds approximately to a location 75% of the spanwise distance as measured from aircraft centerline for typical aircraft. The 70% panel span distance definition is substituted for the ATC parameter described herein. A review of historical aircraft indicates no values of ATC above approximately 40 with the exception of a few low speed high aspect ratio aircraft that do not reach transonic speeds, and supersonic aircraft with sweep angles greater than 50 degrees.
The historical limitation to subsonic speeds for wings of ATC above approximately 40 and low sweep is explained by the fundamental forces that occur to low sweep wings as they experience compressibility effects approaching Mach 1. The lift curve slope (the derivative of lift coefficient with respect to wing angle of attack) increases significantly, generally reaching a maximum peak near Mach 0.95 to 1.0. This phenomenon increases the loads due to wind gusts and the forces tending to make a long thin wing diverge or flutter. In the case of a low sweep wing, the lift curve slope and associated gust loads increase by approximately 50% at Mach 0.95 relative to Mach 0.80. Aircraft generally must be designed by regulation to be flutter and divergence free at speeds 15% above the dive speed (Vd), which in turn is generally 0.07 Mach above the maximum design cruise speed (Mmo). Thus, aircraft designed to cruise above approximately Mach 0.80 must be designed to be flutter and divergence free up to this peak lift curve slope zone near Mach 1, requiring a combination of a structural weight penalty, thicker airfoil sections or shorter span resulting in reduced net efficiency. Progressively higher sweep angles with design cruise Mach numbers have been the traditional means to allow greater wing thickness for a given Mach number in order to minimize structural weight penalties.
Supersonic aircraft must traverse this critical transonic regime; however the high sweep angle typically used to date for such aircraft reduces the peak lift curve slope occurring near Mach 1, reducing the weight penalty for wing strengthening and stiffening. For example a 6/1 aspect ratio 35 degree sweep wing exhibits approximately 82% of the peak lift curve slope of a 15 degree sweep, and a 45 degree sweep reduces this to 65%.
As described in prior U.S. Pat. No. 7,000,870, “LAMINAR FLOW WING FOR TRANSONIC CRUISE”, however, there are significant aerodynamic gains for wings of leading edge sweep angles between 0 and 35 degrees. First, it is feasible to reduce the boundary layer cross-flows fostering long runs of laminar flow which reduces the viscous drag. Second, the lower sweep wings exhibit reductions in lift-dependent drag in the proximity of Mach 1. This reduction in lift-dependent drag in the transonic regime is related directly to the same compressibility phenomenon that increases the lift curve slope and airloads the wing must be designed to resist.
A significant factor in designing wings that must operate in the transonic range has been the difficulty in reliably predicting the aerodynamic loads in the critical regime near Mach 1, and applying those loads to elastic structural finite element models (FEM). Recent improvements in computational fluid dynamics (CFD) codes and FEM's has allowed the design alternatives to be better understood in this critical non-linear transonic regime, and is of importance to designing reduced sweep transonic and supersonic aircraft wings.
Applicant herein has recently conducted aero-elastic wing design and structural analysis of a thin supersonic low sweep wing with a relatively high ATC value of 66, and found through advanced methods and structural tailoring that the aerodynamic advantages of lower sweep thin wings can be provided to more than offset the weight penalties of such wings.
NLF wings having an ATC parameter (combinations of aspect ratio and thickness as defined above) greater than about 45 will be able to fill a gap in efficient cruise Mach number between about 0.80 and 0.95. For example, a low sweep wing with Mach 0.82 design cruise and a 9% t/c airfoil, would enable an increase in feasible aspect ratio from about 8.5 to 12 or greater. Whereas a current aircraft in this general design space (Learjet) has a wing aspect ratio of 7.2.
Another example is a new long range executive aircraft (Gulfstream 650) designed for an efficient cruise speed of Mach 0.85 and a maximum cruise speed of Mach 0.925. It incorporates a wing of 7.7 aspect ratio and 36 degrees of leading edge sweep that is too great to foster significant laminar flow. With the herein invention, a wing of the same aspect ratio and cruise Mach number could be provided with reduced outboard thickness and 20 degree leading edge sweep, fostering significant laminar flow. Such wings can be provided for extensive NLF if the leading edge sweep is less than about 20 degrees by methods described herein and in our patent application referenced above, of which this is a continuation.
An important consideration in the ability to use wings of reduced sweep and drag at transonic and supersonic speeds is significant waisting of the aircraft fuselage and propulsion nacelle bodies in proximity to the wing in accordance with the area-rule. This allows significantly thicker wing t/c on the proximate 50% inboard span to provide the needed strength and stiffness of the wing at acceptable weight.
In addition, certain wing design criteria have been found to enable efficient cruise Mach numbers above 0.95 up to about 1.05, which is beyond the maximum efficient cruise Mach number of current high speed, long range aircraft. Such improved wings could require or would incorporate outboard t/c ratio of about 0.05 to less than 0.03 combined with aspect ratios greater than 6 and 3 respectively, in combination with greater leading edge sweep than the previous limit of about 20 degrees specified in U.S. Pat. No. 7,000,870. For example, a sweep of about 24 to 30 degrees and 3 to 4% t/c is indicated for an efficient cruise Mach number of 0.95; and a Mach 1.05 cruise speed indicates a 18 to 24 degree leading edge sweep and 2 to 3% outboard t/c. Achieving extensive NLF for such a wing sweep is more difficult and some loss in LF coverage extent is expected.
As previously noted in referenced parent patent application (Ser. No. 12,589,424), a number of considerations may drive the wing optimal thickness to higher values, even at the expense of a moderate increase in volume wave drag for a given design Mach number. For example the favorable pressure gradient, which stabilizes the wing laminar boundary layer, increases with t/c ratio, and as noted, structural weight decreases with increasing thickness. In addition, the volume wave drag attributable to the wing can be reduced by contouring the fuselage in the vicinity of the wing. Finally, the achievement of NLF on large areas of the wing surface is dependent on (a) achieving appropriate pressure gradients over the affected surfaces of the wing and (b) suitable leading edge size and shape. These pressure gradients depend not only on the local airfoil shapes, but also are influenced by the fuselage contours adjacent to the wing. There is, accordingly, need for improvements in transonic long range aircraft, and particularly in the optimization of the wing, airfoil shape and thickness, and wing aspect ratio, as well as the fuselage contours affecting both volume wave drag and NLF extent over the wing surfaces. Similar considerations can be applied to the design of horizontal and vertical tail surfaces.
Application Ser. No. 12/589,424 filed Oct. 26, 2009 is incorporated herein, by reference.